The invention relates to semiconductor processing and the prediction of structures and properties resulting from processes used in the preparation and modification of semiconductor materials.
In order to maximize the performance and value of electronic devices including memories, central processor units (CPUs), transmitters and detectors of electromagnetic and sonic radiation, and other components of electronic computers, it is important to reduce the size, noise, and reproducibility while increasing the speed of the devices. This requires growing complex heterostructures in which various dopants are introduced into precise locations and processed to obtain desired distributions, electrical activity, and other properties useful in devices. To optimize the performance of these devices, it is necessary to model and simulate the electrical and mechanical properties resulting from various distributions and clustering of the dopants, oxidation products, and impurities. With previous technologies, modeling and simulation techniques have generally treated the materials as a macroscopic continuum, with continuous variations in concentrations of dopants and, and have used finite element analysis to describe the diffusion and operation of the devices.
In future generations of devices, the size of device elements (for example the gate of a field effect transistor (FET)) will be in the range of less than 100 nm, where it will be important to consider the atomistic characteristics of the materials, rather than just their macroscopic continuum properties. For example, to make a p-type silicon FET with gates less than 100 nm, it is useful to carry out ultrashallow ion implantation deposition of boron, using low energies (e.g., xcx9c1 keV) that limit the boron to a region within a short distance (e.g., 20 nm) of the surface. To obtain optimal activity, it is useful to deposit sufficiently high boron surface concentrations (e.g., 5xc3x971020) near the surface to obtain sufficient activity of dopants for optimum performance. However, it is found that such conditions may lead to a clustering of the dopants and of other defects (vacancies and interstitials) and to long-range diffusion tails that degrade the performance, whereas it is desired to maintain the boron near the surface while unclustered in a substitutional site that maximizes performance. In addition it can happen that too much of the boron near the surface may diffuse to the interface, resulting in a kink or non-optimum distribution in the boron distribution. Also, much of the boron may not have the proper electrical activity (as a low energy acceptor level) due to clustering or association with a non-optimum site. These examples consider boron because there are serious problems today involving such systems; however, similar problem can occur for other dopants.
In order to develop the highest performance devices, it is important to accurately predict such properties as the distribution of the dopants and defects (e.g., vacancies, interstitials) as a function of depositing conditions and subsequent heat treatments (e.g. annealing), oxidation, exposure to other impurities or dopants, changes in external conditions (pressure, stress, voltage, magnetic fields, electromagnetic radiation, ultrasonic radiation, etc.). In addition, it is important to predict the electrical activity and other device properties resulting from the deposition and processing of such systems. Also, it is important to predict the critical voltages and fields for electrical or mechanical breakdown of such systems. In addition, it is important to predict the effects of aging (repeated cycling of voltages, stresses, temperature, and exposure to radiation, oxygen, water, and other molecules).
The invention provides a prescription for a strategy and provides the associated computational techniques for predicting from first principles the structures and properties of electronic materials as a function of processing and operating conditions. These techniques can include quantum mechanics, development of force fields (FF) from the quantum mechanics (QM) or experiment, molecular dynamics (MD) using such FF or using QM, continuum mechanics based on parameters extracted from the molecular dynamics (MD) and elsewhere, and, preferably, combinations of two or more of these. Quantum mechanics (QM) calculations can be used to predict the electronic states and structures of the materials likely to be constructed for various processing conditions of interest. This includes various dopants (e.g., B or P), impurities (e.g. H and O) and defects (e.g. vacancies and interstitials) that might result from the synthesis and processing of the materials. The QM and can provide information on the rates of diffusion of the various impurities and defects and of formation of clusters and other structures. Using molecular dynamics techniques, fundamental rate parameter data from such quantum mechanics calculations or other sources can be used to estimate rates of processes such as diffusion, association and dissociation for collective systems (which can include, e.g., microscopic, mesoscale and macroscopic systems) that contain distributions of several or many kinds of defects and/or impurities. Finally, using continuum mechanics this data, and the fundamental data (e.g., from quantum mechanical and MD calculations), can be used to predict the distributions of dopant and defect structures and clusters as a function of external conditions.
In general, in one aspect, the invention provides methods and apparatus, including computer program apparatus, implementing techniques for predicting the behavior of dopant and defect components in a substrate lattice formed from a substrate material. The techniques include obtaining fundamental data for a set of microscopic processes that can occur during one or more material processing operations, and predicting a distribution of dopant and defect components in the substrate lattice based on the fundamental data and a set of external conditions. The fundamental data includes data representing the kinetics of processes in the set of microscopic processes and the energetics and structure of possible states in the material processing operations. The distribution of each first component is predicted by calculating the concentration of the first component for a time period before the first component reaches a pseudo steady state by solving a first relationship and calculating the concentration of the first component for a time period after the first component reaches the pseudo steady state by solving a second relationship based on one or more second components. The pseudo steady state is a state in which the concentration of the fast component is determined by concentrations of the second components.
Particular implementations can include one or more of the following features. The first components can include fast components having a high diffusivity or a high dissociation rate. The second components can include slow components having a low diffusivity or a low dissociation rate. For each of the first components, the first relationship can be solved with a time step determined based on the diffusivity and the dissociation rate of the corresponding first component. The first relationship can be an equation:             ∂              C        k                    ∂      t        =            ∇              (                              D            k                    ⁢                      ∇                          C              k                                      )              +                  K                  R          ,          ij                    ⁢              C        i            ⁢              C        j              +                  K                  D          ,          m                    ⁢              C        m              -                  K                  R          ,          kl                    ⁢              C        k            ⁢              C        l              -                  K                  D          ,          k                    ⁢              C        k            
where Dk and Ck are the mobility and the concentration of a component k, respectively. In this equation, the first term in the right-hand side represents diffusion of the component k; the second and third terms represents generation of the component k by i+j clustering (i+jxe2x86x92k) and m dissolution (mxe2x86x92k+l), respectively; and the fourth and fifth terms represent destruction of the component k by (k+lxe2x86x92m) and (kxe2x86x92i+j), respectively. The clustering and dissolution coefficients are given by
KR,ij=4xcfx80Rp(Di+Dj) 
KD,k=(nH/4)KR,ijexp(xe2x88x92Eb,k/kBT) 
where Rp is the capture radius, nH is the concentration of lattice sites in the substrate lattice, Eb is the dissociation energy of k into i and j, kB is the Boltzmann constant, and T is the substrate temperature of the substrate lattice. The second relationship can be given by equation:
∇(Dk∇Ck)+KR,ijCiCj+KD,mCmxe2x88x92KR,klCkClxe2x88x92KD,kCk=0 
The techniques can also include calculating reaction information based on the fundamental data. The reaction information can identify major components and reactions from a set of possible components, and major reaction pathways for the processes of the set of microscopic processes. The distribution of dopant and defect components in the substrate lattice can then be predicted based on the fundamental data, the external conditions and the reaction information.
The microscopic processes can include, for example, diffusion, clustering and dissociation of dopant and/or defect components in the substrate lattice. The fundamental data can include, for example, data representing the dissolution rate of defect components, the mobility of mobile species and the binding energy of clusters. The set of external conditions can include initial concentrations for each dopant and defect component, and an initial temperature. The material processing operations can include, for example, heat treatments, oxidation, exposure to impurities, or changes in pressure, stress, voltage, magnetic fields, electromagnetic radiation or ultrasonic radiation.
The fundamental data can be calculated in a quantum mechanics calculation. The reaction information can be calculated in a kinetic Monte Carlo simulation. Predicting the distribution of dopant and defect components in the substrate lattice can include predicting a plurality of distributions of dopant and defect components in the substrate lattice for each of a plurality of different sets of external conditions. The techniques can also include selecting a desired distribution from the predicted distributions, and controlling a manufacturing process based on the set of external conditions corresponding to the selected distribution. The material processing operations can define a procedure for boron doping of silicon substrates, and the set of microscopic processes include the formation, diffusion and dissolution of substitutional boron-interstitial boron pairs in a silicon substrate lattice.
In preferred implementations, the invention thus provides techniques for predicting the structures and properties, such as distribution and clustering of dopants and impurities, that result from implantation, annealing, and other processes for preparing and modifying materials, and for predicting the electrical activity of the system as a function of processing conditions, manufacturing, aging, and application of external fields and conditions. These techniques can be implemented to realize one or more of the following advantages. Accurate prediction of such properties as the distribution of the dopants and defects, electrical activity, critical voltages and fields for electrical or mechanical breakdown, and the effects of aging, and modeling and simulating the structures and properties of devices as a function processing and operating conditions, can make possible the design of improved composition and processing conditions to develop improved properties, reliability and aging, while minimizing cost and failure. Using these techniques to monitor one or more device characteristics during production and compare the monitored characteristics to predicted optima can make possible the incorporation of increased automation into control systems for operating the processes. Prediction of performance as a function of aging and operating conditions can make it possible to develop improved fault tolerant systems.
The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.
The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.